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The separate universe technique provides a means of establishing consistencyrelations between short wavelength observables and the long wavelength matterdensity fluctuations within which they evolve by absorbing the latter into thecosmological background. We extend it to cases where non-gravitational forcesintroduce a Jeans scale in other species like dynamical dark energy or massiveneutrinos. The technique matches the synchronous gauge matter densityfluctuations to the local expansion using the acceleration equation andaccounts for the temporal nonlocality and scale dependence of the longwavelength response of small scale matter observables, e.g. the nonlinear powerspectrum, halo abundance and the implied halo bias, and $N$-point correlationfunctions. Above the Jeans scale, the local Friedmann equation relates theexpansion to real energy densities and a curvature that is constant in comovingcoordinates. Below the Jeans scale, the curvature evolves and acts like a fakedensity component. In all cases, the matter evolution on small scales iscorrectly modeled as we illustrate using scalar field dark energy withadiabatic or isocurvature initial conditions across the Jeans scale set by itsfinite sound speed.

Separating the Universe into the Real and Fake